Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x-6y &= 2 \\ 6x+8y &= -1\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $6x = -8y-1$ Divide both sides by $6$ to isolate $x$ $x = {-\dfrac{4}{3}y - \dfrac{1}{6}}$ Substitute this expression for $x$ in the first equation. $3({-\dfrac{4}{3}y - \dfrac{1}{6}}) - 6y = 2$ $-4y - \dfrac{1}{2} - 6y = 2$ Simplify by combining terms, then solve for $y$ $-10y - \dfrac{1}{2} = 2$ $-10y = \dfrac{5}{2}$ $y = -\dfrac{1}{4}$ Substitute $-\dfrac{1}{4}$ for $y$ in the top equation. $3x-6( -\dfrac{1}{4}) = 2$ $3x+\dfrac{3}{2} = 2$ $3x = \dfrac{1}{2}$ $x = \dfrac{1}{6}$ The solution is $\enspace x = \dfrac{1}{6}, \enspace y = -\dfrac{1}{4}$.